a multiscale analysis of early flower development in arabidopsis … · 2020. 9. 25. · a...

A multiscale analysis of early flower development in Arabidopsis provides an integrated view ofmolecular regulation and growth control

Yassin Refahi1,2,8+,*, Argyris Zardilis1,*, Gaël Michelin3, Raymond Wightman1, Bruno Leggio2, JonathanLegrand2, Emmanuel Faure, Laetitia Vachez2, Alessia Armezzani2, Anne-Evodie Risson2, Feng Zhao2,Pradeep Das2, Nathanaël Prunet4, Elliot Meyerowitz1, 4, 5, Christophe Godin2, Grégoire Malandain3,Henrik Jönsson1, 6, 7+, Jan Traas2+

1The Sainsbury Laboratory, University of Cambridge, Bateman Street, Cambridge, CB2 1LR, UK2Laboratoire RDP, Université de Lyon 1, ENS-Lyon, INRAE, CNRS, UCBL, 69364 Lyon, France3Université Côte d’Azur, Inria, CNRS, I3S, France4Division of Biology, California Institute of Technology, Pasadena, CA 91125, USA5Howard Hughes Medical Institute and Division of Biology and Biological Engineering 156-29,California Institute of Technology, Pasadena, CA 91125, USA6Computational Biology and Biological Physics, Lund University, Sölvegatan 14A, 223 62 Lund,Sweden7Department of Applied Mathematics and Theoretical Physics (DAMTP), University of Cambridge,Cambridge, UK8Université de Reims Champagne Ardenne, INRAE, FARE, UMR A 614, 51097 Reims, France.

+ Authors for correspondence:[email protected], [email protected], [email protected]

* These authors contributed equally to this work

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(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted September 26, 2020. ; https://doi.org/10.1101/2020.09.25.313312doi: bioRxiv preprint

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https://doi.org/10.1101/2020.09.25.313312

Abstract

The link between gene regulation and morphogenesis of multicellular organisms is a fundamental

problem in biology. We address this question in the floral meristem of Arabidopsis, which generates new

tissues and organs through complex changes in growth patterns. Starting from high-resolution time-lapse

images, we generated a comprehensive 4-D atlas of early flower development including cell lineage,

cellular growth rates and the expression patterns of 28 regulatory genes. This information was introduced

in MorphoNet, a web-based open-access platform.

The application of mechanistic computational models indicated that the molecular network based on the

literature only explained a minority of the expression patterns. This was substantially improved by

adding single regulatory hypotheses for individual genes. We next used the integrated information to

correlate growth with the combinatorial expression of multiple genes. This led us to propose a set of

hypotheses for the action of individual genes in morphogenesis, not visible by simply correlating gene

expression and growth. This identified the central transcription factor LEAFY as a potential regulator of

heterogeneous growth, which was supported by quantifying growth patterns in a leafy mutant. By

providing an integrated, multiscale view of flower development, this atlas should represent a

fundamental step towards mechanistic multiscale-scale models of flower development.

Introduction

The loss of function of many regulatory genes causes important perturbations in the growth patterns of

multicellular organisms, which means that they directly or indirectly affect local growth parameters via

the expression of other genes or physical cell properties. The regulatory networks and their dynamics

have been extensively studied in a range of model species (e.g. (Briggs et al., 2018) (Chen et al., 2018)

(Wagner et al., 2018)). This has been an active field of research, in particular with the advent of single

cell sequencing methods, which can now be combined with molecular cell lineage tracking approaches

(e.g. (Cotterell et al., 2020; Frieda et al., 2017)). However, there is often only a partial view of how

growth is coordinated and as a result gene function is usually expressed in general terms such as organ

identity or polarity, referring to their main mutant phenotype in a relatively abstract and qualitative

manner. In addition there are still many open questions regarding the regulatory network structures and it

is often impossible to test their coherence. An important first step towards addressing these problems is

to integrate the existing information on gene expression, and to quantitatively correlate regulatory inputs,

for example in the form of gene expression patterns, with the final output, i.e. shape changes during

development (Coen et al., 2004; Whitewoods and Coen, 2017). This should then provide a solid basis for

more mechanistic studies, involving also the regulation of biochemical interactions and biophysical

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aspects (Abad et al., 2017; Diaz de la Loza and Thompson, 2017; Pasakarnis et al., 2016; Thompson,

1917; Zhu and Roeder, 2020).

We address this question in the floral meristem (FM) of the model plant Arabidopsis, which generates

four whorls of floral organs and is one of the best-characterized morphogenetic systems available

(Blázquez et al., 2006; Bowman et al., 2012; Chen et al., 2018). The function of a range of key genes

together with their domains of expression has mainly been studied on a one by one basis and their

individual function, spatial expression and dynamics have been characterized (Fig. 1, supplementary

table 1). Like the vegetative and inflorescence meristems, the floral meristem contains a population of

stem cells, which are kept in an undifferentiated state by regulatory genes like SHOOTMERISTEMLESS

(STM), WUSCHEL (WUS) and CLAVATA (CLV ) 1-3 ( (Long and Barton, 2000); (Lenhard and Laux,

2003); (Mayer et al., 1998)) . Other genes, like AINTEGUMENTA and MONOPTEROS h ave been more

specifically associated with organ outgrowth ((Krizek, 2009); (Nole-Wilson and Krizek, 2006);

(Yamaguchi et al., 2013)) . During flower formation, yet another set of regulators, including

PHAVOLUTA, PHABULOSA, ASYMMETRIC LEAVES1 and 2, FILAMENTOUS FLOWER and ETTIN ,

determines the abaxial/adaxial (dorso-ventral) polarity of the organs, i.e. the identity of the cells next to

and further away from the shoot meristem ((Emery et al., 2003); (Iwakawa et al., 2007); (Machida et al.,

2015; Sawa et al., 1999a); (McConnell et al., 2001); (Sawa et al., 1999b); (Sessions et al., 1997)) . The

floral organs are separated by boundary domains characterized by the expression of notably the CUP

SHAPED COTYLEDON (CUC) 1-3 g enes ( (Aida et al., 1997); (Hibara et al., 2006)) . The spatial and

temporal regulation also involves several hormones, including cytokinin and auxin ( (Besnard et al.,

2014a) (Reinhardt et al., 2003)) . Cytokinin has been mainly associated with meristematic activity,

whereas auxin is required for organ positioning and outgrowth. While the previous regulators can also be

found in vegetative meristems, a major subnetwork, including the transcription factors L EAFY (LFY),

APETALA (AP) 1-3, PISTILLATA (PI), AGAMOUS (AG) and SEPALLATA (SEP) 1-4, is involved in

defining the type of organs to be produced ((Blázquez et al., 2006; Krizek and Fletcher, 2005) ; (Goto and

Meyerowitz, 1994); (Kaufmann et al., 2009); (Ó’Maoiléidigh et al., 2014); (Parcy et al., 1998); (Pelaz et

al., 2000); (Wuest et al., 2012); (Thomson and Wellmer, 2019)) .

The general architecture of this network and parts thereof have been studied and models for

molecular regulation have been proposed (e.g.: (Sánchez-Corrales et al., 2010); (La Rota et al., 2011);

(Chen et al., 2018). However, in spite of this extensive body of knowledge, our understanding of how

the network orchestrates flower morphogenesis remains fragmentary. The coherence of the existing data

needs to be tested, while a more integrated, multiscale view at the level of the whole system is missing.

This not only implies a need for a better knowledge of how the network is behaving in time and space at

cellular resolution. In addition the network dynamics need to be correlated with growth patterns.

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We used high-resolution time-lapse images to generate a comprehensive 4-D atlas of early flower

development, including the expression patterns of 28 regulatory genes. This integrated view allowed us

to test the coherence of the published data on molecular regulation. A quantitative correlation analysis

between gene expression patterns and growth patterns then led us to propose a set of hypotheses for the

combinatorial action of regulatory genes in patterning and morphogenesis. Hypotheses concerning the

central regulator LEAFY were tested experimentally, which supported a role in growth control both

during sepal initiation and organ boundary formation.

The results were made available in the form of an interactive web-based atlas using a dedicated online

tool called ‘Morphonet’ (http://morphonet.org, (Leggio et al., 2019) ) that can be accessed and further

developed by the entire scientific community.

Results

High-resolution live imaging of flower development reveals consistency in shape and size

We used confocal microscopy to live image flower primordia from initiation to stage 4 when the sepals

start to overlie the flower meristem and all four whorls have been specified (Smyth et al., 1990). This

was done using a yellow fluorescent protein (YFP) targeted to the plasma membrane or using the

membrane specific dye FM 4-64 (see Methods, (Fernandez et al., 2010; Willis et al., 2016) ).

The development of six meristems (FM1-6) was recorded in a total of 50 3-D image-stacks, followed by

cell segmentation and lineage tracking (Methods, Fig 2, Fig S1). In flower meristems, cell division

patterns are not fixed, in contrast to e.g. roots or hypocotyls (Montenegro-Johnson et al., 2015). It is,

therefore, not straightforward to compute an average time course, including cell lineage information

which is essential to study the correlation between cellular dynamics and gene expression. For this

reason we aimed to select a representative series for further analysis. To this end, we compared the shape

of all 6 meristems during development. Since there is no obvious way to synchronise flower

development and the geometrical shape of individual time points of one series does not exactly

correspond to the time points of other series. To circumvent these problems, we applied a registration

method to align and compare different acquisition sets using the surface of flower primordia, represented

by a point cloud, as the overall shape mesure (Methods, (Michelin et al., 2016)) The quantitative

assessment of the variability in shape and size of the flower primordia captured in sequences FM1-4 and

FM6 illustrated that they go through similar developmental stages with consistent shapes and sizes (Fig.

S2 and S3), while it was not possible to compare the shape of FM5 reliably with that of the other

meristems (Fig. S3). This motivated the choice of FM1, which had the highest temporal resolution and

spanned floral development from initiation to stage 4, as a representative reference. To facilitate further

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analysis, this time series was added to the web-based browser MorphoNet (http://morphonet.org/,

Methods, (Leggio et al., 2019)).

An integrated view of gene expression patterns provides a high-resolution spatiotemporal

differentiation map of flower development

We next included the expression patterns of 28 important genes involved in floral meristem function,

organ identity, organ outgrowth and organ polarity in the 4-D template (Figs. 1, 3A,B). For 21 genes, the

often partial published information was complemented by our own results coming from RNA in situ

hybridization or confocal live-imaging (Methods). The collected patterns were integrated into the FM1

time course by manually annotating individual cells using the tools available via MorphoNet (Methods,

Figs S4-S6, Supplemental file for justification of individual genes). For this purpose 5 distinct stages of

development were chosen (as defined by (Smyth et al., 1990)): the initium stage (called here stage 0) and

stage 1 to stage 4 (Fig 3B). We chose to perform a binary labelling, i.e. to indicate only the presence or

absence of gene expression, given the predominant qualitative nature of the available expression data.

The single gene expression patterns (‘gene patterns’) were then combined. We could thus identify cell

groups that expressed unique gene combinations and corresponded to specific differentiation states,

termed ‘cell states’. 28 cell states were present in both L1 and L2 (not taking into account the L1

marker ATML1) and 3 L2-specific states were found (Fig. 3). We next conducted an exploratory data

analysis using unsupervised hierarchical clustering, (Methods), to generate a cell state similarity map

using Hamming distances, i.e. the number of gene expressions which differ between cell states, as the

measure of similarity (Fig. 3C-D). The dendrogram revealed clusters of states, which formed different

functional groups of cells through flower development (Fig. 3D, Supplementary Table 2). These

included, for example, meristematic cells, boundary cells, as well as cells expressing genes defining

polarity or organ primordia. Similarities in expression between alternative cell fates were identified at

high resolution, e.g. connecting the boundary domain with the expression domains where petals and

anthers are initiated (Fig 3D: boundary cluster, containing states 4, 20, 30, 19, 25 and 29). To investigate

the temporal evolution or cell-differentiation paths of the cell states in the outer cell layer, we used the

computed cell lineages and built a weighted directed cell state ‘transition graph’ where the nodes are

the cell states (Fig. 4, Methods). The graph reveals a core of ‘stem cells’ at the adaxial domain of the

bud at stage 1 (State 7), providing all cell types of the flower at stage 4. This is similar to typical tree-like

differentiation paths often described for mammalian development (Enver et al., 2009). Similarly, at stage

2, State 7 has split up in sepal ‘precursors’ and the central meristematic domain (State 10), which will

give rise to all other states. However, the plasticity of plant cells is clearly represented where several cell

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types contribute to future stages. For example, sepal tip cells come from all cell states present at stages 0

and 1. Descendants of both bract (State 5) and SAM boundary cells (State 4) contribute to the same cell

state at later stages, although being quite different in terms of their original expression patterns.

Adding single regulatory hypotheses for individual genes substantially improves gene patternpredictions

We next examined alternative hypotheses to quantitatively explain these gene expression patterns (Fig.

5). We first analyzed the possibility of the patterns being driven mainly by the lineage, i.e. whether the

gene expression at an earlier time point can be used to predict the expression at a later time point. This

led to relatively good predictions at early and late stages, but was less successful for transitions between

intermediate stages (Fig. 5B-C), as measured by a Balanced Accuracy score (BAcc), combining the

normalised false positive and false negative rates (Methods). This indicates that most regulatory

interactions have an effect during the end of stage 2 and stage 3. For example, for over 75% of the genes

we found a BAcc score larger than 0.75 (closer to a perfect pattern than to a random pattern) when

following lineages from stage 0 to 1 or from 3 to 4, while this was only true for less than 20% of the

genes when cells were followed from stage 2 to 3 (Fig. 5B-C). The result was highly variable between

genes and also between individual time points for single genes (Fig. 5B).

We next tested whether the literature-derived network (Fig. 1) could account for the expression patterns

of single genes. To do this, we modelled the gene regulatory network using a set of boolean rules

combining activating and repressing inputs suggested by the literature, and combined them in all

possible ways using logical ‘AND’ and ‘OR’ rules (Methods). This produced a ranked list of alternative

logical combinations for each gene regulation and the combination(s) with the best similarity with the

gene expression pattern at hand were selected (Methods, Supplemental Table S3). For comparison, we

also used the input regulatory arrows from the literature network but selected random genes as inputs

(Fig. 5B-C, Methods). The literature-based regulatory network improved the ability to explain a number

of gene expression patterns, in particular during the last two stages (BAcc increase of 0.22 on average

for stage 3 and 4) compared to the randomized networks (Fig. 5B-C). Several genes, such as LFY and

AG at all time points, AS1 at stages 1, 3-4, and FIL at stage 3 all map perfectly or almost perfectly on

the expression patterns extracted from the literature, indicating that the regulation presented in the

literature matches the patterns well for a subset of genes at certain time points (Fig. 5A-B). However,

this is only true for a minority of genes in the network. While the literature network was, in average,

always performing better than the randomized networks, it was only significant at the later stages 3 and 4

(p-values of 0.09, 0.19, 0.23 for stages 0, 1, 2, respectively compared to 0.04 and 0.008 at stages 3 and 4,

respectively).

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When comparing the literature based regulatory predictions with lineage predictions, the literature-based

regulation did not lead to significant improvements on average at any time point, and lineage even

performed better at stage 4 (Fig. 5D, p-values 0.11, 0.44, 0.46, 0.02 at stages 1, 2, 3, 4, respectively). At

stage 4 for example, the literature-based network only improved the predictions for a small number of

genes such as LFY, AG, and SUP, while the patterns of ANT, the CUC genes, and SEP3 were better

explained by lineage (Fig. 5A-D).

For a large subset of the genes the expression could not be reproduced using the regulatory interactions

provided in the literature nor using lineages, indicating that the regulatory network is not complete. We

therefore investigated how the addition or removal of single regulatory inputs changed the ability to

predict the spatial pattern of each individual gene. This approach identifies the most plausible extra

inputs required to generate the pattern. After testing all additional genes as activators or repressors and

all possible logical combinations with the literature-suggested regulation, we identified the regulations

leading to the best BAcc score for each gene (Methods, Table S4). This increased the predictability of the

gene patterns significantly as compared to using the literature-proposed regulation (p-values 0.012,

0.003, 0.004, <10-3, <10-3 for timepoints at stages 0, 1, 2, 3 and 4 respectively; Fig. 5A-C, E), and

improved the pattern for all but two genes (Fig. 5E).

In summary, our results show that the gene regulatory network provided by the scientific community

only significantly improved the predictability of gene expression patterns compared to random

interactions at late time points. Compared to cell lineage, the published network improved predictability

for a small subset of the genes at specific stages of development only. Significant improvements in

predictability were achieved for gene patterns by adding novel single interactions. When combined, the

added hypotheses represent a plausible coherent mechanistic description of a gene regulatory network

that can explain the gene patterns for early flower development.

Exploring the genetic control of growth patterns

We next investigated the control of growth during development. We therefore first computed the cellular

properties. The distribution of cell sizes in this meristem was in line with previous studies on

Arabidopsis meristems (Fernandez et al., 2010; Gibson et al., 2006, 2011; Jackson et al., 2019; Willis et

al., 2016) (Fig S7), and the number of cell neighbors within the L1 (epidermal) and L2 (subepidermal)

layers was in line with previous studies on plants and animals, (Lewis, 1926) (Gibson et al., 2006, 2011;

Jackson et al., 2019; Willis et al., 2016) (Fig S8).

Using cell lineage information, we computed growth rates and growth anisotropy at cellular resolution

(Fig. 6, Methods). Since absolute expansion rates can fluctuate considerably between individual flowers

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and throughout development (Figs. S1 and S2), we focused on relative growth rates and directions

between consecutive time points (Figs. 6A). Relative differences in growth rate were particularly striking

at stage 3 and 4, when the sepals start to grow out (Fig. 6A, (Smyth et al., 1990)). The analysis of growth

directions showed that cells start to grow anisotropically when the sepals are initiated. This was

particularly evident on the abaxial side at stage 4, when these organs begin to cover the flower meristem

(Fig 6B).

Although all of the genes considered here are involved in growth regulation at some level, it is unknown

where, when and to what extent they regulate growth rates and directions. To obtain further information

on their roles, we next correlated the growth patterns with gene expression. To quantitatively compare

the growth rates of different cell populations we introduced a ‘relative growth difference’ (RGD)

defined as (g1-g2)/(g1+g2), where g1 and g2 are the median growth rates within the two populations

(Methods). A limited number of individual genes can be consistently connected to low or high relative

growth rates (Fig. 7A). The gene expressed in cells with the highest median growth rate is AHP6 (RGD

>0.07 and p-value < 0.001 when compared with all other genes). This gene has been linked to organ

initiation (Besnard et al., 2014b), and is never connected to slowly growing cells. Conversely, CUC1-3

expressing cells are correlated with slow growth (RGD < 0.4, p-value < 0.003). By contrast, most

expression domains show very broad distributions of growth rates indicating no instructive information

and several genes have a double-peak distribution.

Cell states are better correlated with growth patterns with more spread between the growth distributions

(Fig 7B, cf. Fig 7A). In particular, cell states 26 and 27 (RGD > 0.22, p-values <0.001 when compared

with all other states) and their precursor states 16 and 17 (RGD > 0.1, p-values<0.003 when compared to

states except 26 and 27) are fast-growing, identifying the central and abaxial side of the sepal (Fig. 3A,

Figs. 6A, 7B-C). Whereas growth regulation is captured when using the cell state information, it is not

trivial to determine the precise gene combination that provides the regulatory motif, in particular since

the analysis of individual gene expression domains did not reveal any strong correlation. We therefore

investigated growth correlations starting from pairwise comparisons of genes that had partial overlapping

expression patterns (Fig. 8). For a pair of genes A and B, the idea was to see if the cells in the states

expressing gene A were growing more slowly or more rapidly in the sub-set of states where they were

co-expressed with gene B. This would identify gene B as having potentially a growth-promoting or

inhibiting activity within the states where A is expressed. At floral stage 4, for example, STM identifies

the slow-growing states 14, 22-24 within the ETTIN domain from the fast-growing states 16 and 27

(RGD = 0.36, Fig. 8A). Similarly, LFY identifies fast growing states within the AP1 domain (RGD =

0.36, Fig. 8A). This analysis was carried out for every gene combination and for every time point, which

relates each individual gene expression pattern to all cell states where it has a differential expression

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(Fig. 8B, Figs. S12-S14). The genes fell into three broad classes: those that were potentially

growth-stimulating, those that were potentially growth-inhibiting and a set that apparently had mixed

effects (Fig. 8B). This confirmed AHP6 and CUC1-3 as potentially growth-promoting and inhibiting,

respectively (cf. Fig. 7A). In addition, genes with very wide growth rate distributions, such as ANT and

LFY came up as potential growth-promoting regulators (Fig. 8B).

In summary, apart from AHP6 and CUC1-3, individual genes could not consistently be connected to

relative growth rates and do not seem to act as dominant growth regulators by themselves. However,

correlating the pairwise expression patterns of all 28 genes with growth patterns, we were able to

propose growth promoting and/or inhibiting activities for a majority of them. Given that we also identify

the combination of genes active in these regions (Figs. S12-S14), gene motifs for growth regulation are

identified that can be included in mechanistic models.

With regard to the control of growth directions, the correlations with the individual gene expression

patterns were not particularly informative. CLV3, PUCHI, SUP, SEP3 and SVP which showed low

degrees of anisotropic growth (Fig. 9A), but many other genes were expressed in domains with relatively

wide distributions. Like for growth rates, the cell states defined much more distinct behaviors. The cell

states of the forming sepal are growing most anisotropically as identified in the transition graph (Figs.

6B and 9C), where the abaxial cells of the developing sepal (cell state 27) were also growing slightly

more anisotropically than the adaxial side (cell state 16, Fig. 9B-C). This puts the polarity genes, in

particular FIL, forward as potential regulators of anisotropic growth. Early time points have relatively

low anisotropies, and there is a transition at stage 2, where the whole lineage coming from cell state 10

has relatively more isotropic growth compared to the sepal structures (Fig. 9C).

Quantitative analysis identifies predefined growth patterns at stage 2.

Growth analysis identified an increase in heterogeneous and anisotropic growth at later stages (Figs

6A,B 8). To understand when this switch can be first identified, we investigated growth over longer time

scales. Considering the growth of cells from early stages (stages 0 and 1) onwards, no obvious spatial

pattern of heterogeneity in the contribution to the final flower was found (Fig. 7D, Fig. S10A). This

shows that at these early stages, the cells will produce a population of descendants of similar size at stage

4 or at least with no clear spatial correlation (Fig. 6D). However, at stage 2, although the flower bud is

still close to a symmetric hemisphere (Figs. 2-3), cells have been committed to become fast or

slow-growing at later stages (Fig. 6C, D), even if the growth rate at this time is quite homogeneous (Fig.

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6A). The same observation was made for two other meristems with longer time series, FM2 and FM6

(Fig. S10 B,C).

This correlates also with the division of the state transition tree at stage 2, where the central state 10 is

defining the central parts of the flower and are highly disconnected from the sepal differentiation

lineages (Fig. 3). At stage 2 cell states 8, 9, 11 and 12 grow at approximately the same rates as the

neighboring domain (cell state 10) (RGD <0.13, p-values > 0.753, Fig. 8C). Still, when comparing the

growth up until stage 4, the descendants of these four cell states grow much faster (RGD>0.19, p-value

<0.001, Fig. 9C) and hence identify growth precursor states (Figs. 7C, 8C, cf. Fig 6D). By contrast, cell

state 10 has descendant states that are all relatively slow-growing (Fig. 7C).

In conclusion, we identified a transition from a patterning phase with homogeneous growth at stage 2 to

a growth phase, where in particular the sepal lineages increase their growth rates and anisotropy.

Quantitative growth analysis confirms a role of LFY in the coordination of growth between specific

domains.

Cells expressing LFY had one of the broadest growth distributions among all genes (Fig. 7A). Still, the

more detailed analysis of the growth patterns described above, pointed at a prominent role in stimulating

growth during early flower development. Whereas it is well known that LFY is required for the

specification of floral organ identity, its precise role in organ outgrowth remains to be established and

mainly a general role in auxin signalling and patterning has been proposed (Li et al., 2013; Parcy et al.,

1998; Yamaguchi et al., 2014). To test whether LFY has a role in growth during early flower

development, we live-imaged a number of flowers of the strong lfy-12 loss of function line (Fig 10A, Fig

S16, (Maizel and Weigel, 2004) ) during the formation of the four sepal-like organs, i.e. comparable to

the stage 2 to 4 transitions in the wild type. In all three acquisitions, the organs in the medio-lateral

position grew out first, while the adaxial and abaxial primordia followed later and the boundary regions

between sepals were less pronounced. The last sepal-like organ to grow out was slightly misplaced in

one of the series, suggesting the beginning of a spiralled phyllotaxis. To analyse how these

morphological phenotypes relate to growth in cells where LFY is normally expressed, the relative growth

rates in the different domains where LFY was identified as a potential growth promoter were

subsequently compared in one of the time-series for stage 3 and 4 (Fig. 10B, C; cf. Fig. 8, Figs. S13 and

S14). In the mutant, these were defined based on morphology (e.g. negative curvature for the boundary)

and lineage. The differences in growth rates between these zones were reduced in the mutant compared

to wild type at the equivalent of stage 4 (Fig 10B, C) supporting that LFY is positively contributing to

local growth in early flower development. This was true for all zones identified (Fig. 10C), and the cells

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in regions normally expressing LFY had consistently a higher reduction in growth rate compared to the

regions where LFY is not expressed in wild type (Fig. 10D). This was partially due to the delay in

outgrowth of sepal-like organs in the adaxial and abaxial positions in lfy. Whereas the difference

between the boundary zone and sepals was most clearly reduced (30% reduction in median RGD), the

difference between the meristem center and the sepals was less affected (14% reduction in median

RGD).

Discussion

We present here a detailed descriptive and quantitative model of early flower development. Integrating

information at multiple scales, we have established a number of correlations which led us to propose an

important set of testable hypotheses regarding the molecular regulatory network and its link to growth

control. These hypotheses could not have been generated easily using other approaches.

Molecular network dynamics

Based on an extensive analysis of the expression patterns of 28 genes, we propose the existence of at

least 31 cell states in the L1 and L2 layers, which mounts up to 60 by taking into account ATML1,

expressed in the epidermal layer.

Even considering a simple, binary on/off regulation of gene expression, the patterns are so complex that

the analysis of spatial gene regulation becomes impossible based on visual inspection only. We therefore

developed a set of tools to analyze the structural dynamics of the molecular network in space and its

capacity to predict the observed expression patterns. This indicated that the published interaction

network is not complete. Importantly, the addition of a limited set of single regulatory hypotheses not

identified during our literature search significantly improved the predictive power of the network. With

these extra hypotheses, the coarse network structure and composition are in principle sufficient to

explain the observed expression patterns. As a result the proposed network can be a starting point for

mechanistic gene regulatory models describing the developing patterns during early flower development.

A complete set of testable hypotheses ranked by their effect on the predictive power of the model is

given in tables S3 and S4 and we will only discuss here a limited number of striking examples.

As an example, the predictions concerning AHP6 illustrate well the incomplete nature of the available

data. AHP6 has been described as a direct target of MP (Besnard et al., 2014b). Whereas the data

summarized in the atlas are compatible with the hypothesis that MP is required, the latter has a much

broader expression pattern than AHP6, suggesting further regulation. The simple hypothesis that STM

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could act as an inhibitor of expression would substantially improve the predicted pattern. This is in

contrast to the conclusion by Besnard et al (Besnard et al., 2014a) who observed a temporary

co-expression of both genes and concluded that AHP6 was probably not repressed by STM. However,

their observations are also compatible with the hypothesis that STM inhibits AHP6 above a certain

threshold. In that case, the temporary overlap would correspond to the transition of cell state 7 to 8 or 9

to 16, when STM expression diminishes.

Novel hypotheses also resolve potential contradictions in the regulatory network model. The evidence so

far suggests that the maximum levels of LFY and CUC, respectively involved in organ formation and the

establishment of organ boundaries do not overlap (supplemental information). There are indications,

however, that LFY directly activates CUC2 (Yamaguchi et al., 2014). Although this seems contradictory,

several experiments indicate that during early stage 3, LFY is expressed in the future boundary region,

but at a lower level than elsewhere in the developing flower (supplementary data file 1 and 2). Likewise,

CUC2 shows a broader expression pattern than just the boundary region, again at a weaker level. In

parallel, the expression pattern of ANT, an upstream regulator of LFY, is much more complementary to

CUC, and our hypothesis that ANT is a negative regulator of CUC would substantially enhance the

coherence between the predicted and observed patterns (Fig. 6A). This then would lead us to propose the

existence of an incoherent feedforward motif between ANT, LFY, CUC, where ANT positively regulates

CUC via LFY together with the proposed negative direct regulation. This type of motif is common in

biological regulation and can tune the level and timing of expression of the individual genes (Goentoro et

al., 2009); (Gruel et al., 2016).

Gene activity and growth control

A number of genes have been explicitly associated with growth control, in particular during organ

outgrowth (Nole-Wilson et al., 2005; Yamaguchi et al., 2016) ; (Besnard et al., 2014a) ) or in the slowly

growing central zone (Schoof et al., 2000). When looking at the distribution of growth rates for each

gene, this correlation was confirmed only for some cases: AHP6 is always expressed in rapidly growing

cells during early organ formation, whereas the CUC, PUCHI and CLV3 genes (Chandler and Werr,

2017; Hibara et al., 2006; Lenhard and Laux, 2003) are active in the slowly growing domains of the

flower. However, it was not possible to make such direct correlations for other genes supposed to control

morphogenesis (Fig. 7A).

This is well illustrated by the auxin-regulated transcription factor MP and its downstream targets ANT

and LFY have been implicated together with AIL6 in flower morphogenesis (Elliott et al., 1996; Krizek,

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2009; Nole-Wilson and Krizek, 2006; Nole-Wilson et al., 2005; Yamaguchi et al., 2013). There is

convincing evidence that ANT is involved in the control of cell proliferation (Mizukami and Fischer,

2000; Nole-Wilson et al., 2005). It was therefore surprising that ANT expression patterns did at first sight

not correlate with particular growth rates: they are expressed in both slowly and rapidly growing cells

throughout development. We therefore carried out a more detailed analysis taking into account

co-expression in the different cell states, which finally clearly indicated that ANT c ould indeed be

considered as potentially growth-promoting (Fig. 8B). The precise function of LFY and MP in growth

control is less well established. MP loss-of-function leads to reduced flower outgrowth suggesting it

promotes growth, but we found that it was mainly expressed in more slowly growing subpopulations.

This points at a broader role of MP and is in line with some observations that over-expression of MP can

also lead to reduced organ growth (Hardtke and Berleth, 1998). LFY is one of the main regulators of

floral organ initiation and identity. It has been mainly associated with patterning events, and might also

be involved in promoting auxin signalling (Li et al., 2013; Parcy et al., 1998; Yamaguchi et al., 2014).

Although the distribution of growth rates in the LFY domains was again very broad (Fig. 7A), the

combinatorial analysis indicated one of the strongest correlations with rapid growth of all genes tested

(Fig. 8B). We therefore quantitatively analysed the growth patterns in the strong lfy-12 loss of function

mutant at a developmental stage equivalent to stage 3 and 4 in wild type plants. At the equivalent of

stage 3 in the mutant, all four sepal-like organ primordia are marked by a local increase in auxin

signalling, as revealed by the auxin inducible promoter DR5 (Yamaguchi et al., 2014), but we found that

in particular organs in the abaxial and adaxial positions grow out later than the medio-lateral primordia,

in contrast to the wild type. In addition, the differences in growth rates between the boundary and the

adjacent zones is reduced, mainly when comparing stage 4 wild type flowers with an equivalent stage in

lfy-12. The quantitative analysis, therefore, further supports the hypothesis that LFY is involved in

coordinating cell expansion rates within specific subdomains, in particular to maintain sufficient growth

rate differences between the sepals and sepal boundaries. The relative weak modifications in growth

patterns might at first sight not seem significant. However, In terms of volume doubling times, the sepals

in the wild type would achieve volume doubling two times faster than the boundary cells. In lfy-12 this

would be reduced to 1,6 times faster. Since growth is exponential and doubling times are in the order of

24h, these changes have the potential to induce substantial changes in organ shape over a few days.

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Conclusion

The integrated analysis of early flower development presented here suggests a number of further steps

forward. The dataset can be easily extended by adding new expression patterns or expression gradients.

By providing a dynamic template, it should be very useful in interpreting single cell sequencing efforts,

which are precisely missing this type of detailed spatial information. The online atlas can also be

enriched by information of different nature, including for instance cell polarity or mechanical properties.

Other templates, coming from different time-series of wild type and mutants, can be added for further

quantitative comparison as we show here for lfy. The ultimate aim would be to produce an artificial

flower template using average behavior, or a collection of templates providing information on the

variability existing in flower development. The atlas also provides an essential step towards the

development of complex mechanistic models. Using the multiscale data of the atlas as input, it now

becomes possible to compare quantitatively the results obtained in vivo with those coming from

simulation where a large range of hypotheses can be tested in parallel, as we showed with boolean

models here. Importantly, the interactive atlas is available online and provides a tool that can be used and

further developed by the entire scientific community.

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Methods

Live imaging

For clearly visualising cell edges for subsequent segmentation, we either used Arabidopsis thaliana

(Col-0) plants containing a modified Yellow Fluorescent Protein (YFP) that is acylated and localised to

the cell membrane (Willis et al., 2016) or staining with FM4-64. lfy-12 (Columbia background, (Maizel

and Weigel, 2004) ) mutants were imaged after staining with FM4-64. Plants, grown in short days under

standard conditions, were removed from soil soon after the transition to reproductive growth when the

length of the inflorescence stem was less than 1 cm. These small plantlets, including roots, were

carefully transferred into a plastic box containing molten, cooled 1% w/v agar supplemented with 2.2

grams l−1 MS salts and Gamborg B5 vitamins. Meristems were then dissected to remove obstructing

flowers, the box filled with water and then imaged using either a Zeiss LSM780 or LSM700 upright

confocal microscope with a 20x or 40x water dipping objective. Confocal Z-stacks were taken of

primordia and detector pixel format, slice interval and zoom were set so that each resulting voxel is less

than 300 nm3, as specified in the data set provided online (doi: provided on acceptance). Plants were

transferred to the growth chamber between successive acquisitions.

Segmentation and lineage tracking

Z-stacks of 2D (x-y) optical sections of five primordia expressing YFP were collected (numbered as

FM1-5). A sixth meristem (FM6) was imaged after staining with FM4-64.

During confocal imaging of primordia, the flowers moved upwards due to meristem growth and stem

elongation which led to oversampling of confocal optical sections in z-direction and an artificially

stretched primordium after 3D reconstruction (Fig S11). To correct this artefact, we first manually

selected cells on the epidermal layer whose thickness were least affected by the movement in z-direction

(whose anticlinal wall normal were pointing close to the x-y plane direction). We then computed the

average cell thickness of the selected cells ( ). We then selected the epidermal cells whose𝐿1𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠

thickness were the most affected by the movement (whose anticlinal wall normal were pointing close to

the z-axis) and computed their thickness ( ). To correct the artefact, we divided the voxel𝐿1𝑠𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠

thickness by , see Figure S11. On a few time points, we also performed a rapid(𝐿1𝑠𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠

)/ 𝐿1𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠

scan, where only two sections were made, to determine the height (in the Z-direction) of the flower bud

as growth was negligible then (see also: (Willis et al., 2016)). These new estimations were close to the

values calculated previously (<5%).

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To quantify growth, we used the high-throughput 4D (space + time) image segmentation and tracking

pipeline that we previously developed (Willis et al., 2016). This 4D imaging pipeline allows precise

quantification of cellular growth over multiple cellular generations using MARS-ALT (Fernandez et al.,

2010). Using the collection of image stacks, we used a three-dimensional auto-seeded watershed

algorithm (Fernandez et al., 2010) to segment the cells. The segmented images were manually checked

for segmentation errors (over-segmentation, under-segmentation, missing cell, or shape error). For this

purpose, we conducted a visual inspection of segmentation quality of two dimensional (x-y) optical

sections by comparing the optical section obtained using a confocal microscope and corresponding

segmentation. In case of segmentation error, the contours of the cells were corrected on 2D sections. Cell

volumes were calculated by voxel counting and multiplying this count by the voxel volume.

To track mother-daughter cell lineages, we first performed an affine transformation followed by a

nonlinear registration using a block-matching framework (Commowick et al., 2008; Malandain and

Michelin, 2017; Michelin et al., 2016) between two successive confocal acquisitions which computed the

deformation field between them. Using this deformation field, we used ALT (Automatic Lineage

Tracking) (Fernandez et al., 2010) to compute cell lineages, between consecutive segmented time points.

The mother-daughter pairings were further inspected for errors and manually corrected and validated for

L1 and L2 layers, see Figs. 2 and S1.

Comparison Floral Meristems

We used the surface of flower primordia, represented by a point cloud, as the overall shape to compare

the six sets of acquisitions. Although they go through similar developmental stages, each primordium has

different cell arrangements. Also, there is no obvious way to synchronise flower development and hence

the geometrical shape of individual time points of one series do not exactly correspond to the time points

of other series. Therefore, we first computed the spatial and temporal correspondence between the six

time series by quantifying shape differences (Michelin et al., 2016). The method uses a rigid

transformation based on the hypothesis that two primordia at the same developmental stage have similar

size and global shape. Since the shape of the flower primordium does not change sufficiently during

stage 1 and 2 for such a comparison, we examined the overall shape changes during stage 3 and 4, when

the sepals grow out and more dramatic changes in geometry are observed. To facilitate comparison, the

temporal resolution of each time course was first refined to one hour using a dedicated 3D image

interpolation method (Malandain and Michelin, 2017).

Integration of the gene atlas into Morphonet and AtlasViewer

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For online display and the introduction of expression patterns, Morphonet was used

(http://www.morphonet.org). For access see supplemental information. Morphonet is a web-based

interactive platform for visualization and sharing of complex morphological data and metadata (Leggio

et al., 2019). Exploiting its Unity (https://unity.com) 3D visual engine, it offers a vast assortment of

possible interactions with 2, 3 and 4D datasets. Through a flexible hierarchical representation of

biological structures and dedicated formats for associated metadata, users can follow the dynamics of

biological shapes, onto which associated quantitative and qualitative properties can be projected.

Cells are represented with meshes in Morphonet, and the meshes generated from the cell segmentation

were converted to obj format and uploaded to Morphonet together with lineage information.

For the introduction of gene expression patterns, five time points were chosen (Fig. 3, (Smyth et al.,

1990) corresponding to:

- the initium stage,

- stage 1 (the flower starts to bulge out),

- stage 2 (a globular bud is formed, separated from the inflorescence meristem),

- stage 3 (the ab- and adaxial sepals start to grow out)

- stage 4 (all sepals are clearly growing out and the four whorls have been specified).

The expression patterns of 28 genes were subsequently introduced. This was in short done as follows

(see also Supplementary Information):

1. Collection of data from the literature. As many available image sets as possible were

collected from the literature. This included GFP expression patterns and RNA in situ

hybridizations.

2. Complete existing data with new data. We completed these data by our own RNA in situ

hybridizations. For this purpose, we generated a further 60 sets of serial sections with the

expression patterns of 20 genes (Original data available online (doi: provided upon

acceptance), Supplementary Information).

3. Manual annotation of timepoints. To facilitate interpretation, we used a binary notation (i.e.

genes are either on or off). Since often only 2D data in the form of sections were available

and published 3D GFP data were usually partial, it was not possible to project directly the

patterns automatically on the atlas. Instead, we used a manual protocol using the annotation

tool in Morphonet by clicking on the individual cells. Cells potentially expressing a

particular gene were identified by manually projecting sections of in situ hybridizations or

confocal sections on the different time points of the atlas. Whenever possible, cell numbers

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were counted to estimate the size of the expression pattern. For each gene 2-4 datasets

available in the literature were identified. We encountered three different cases:

i. The patterns of the in situ hybridization and/or GFP were simple to interpret, and zones of

expression could be unambiguously identified (Fig S3). In the absence of GFP patterns, the

use of serial sections was crucial.

ii. There was a conflict between results obtained using GFP expression and in situ

hybridizations. In that case, the in situ hybridization results were used (Fig S4).

iii. If information on both protein levels and RNA levels were available, the RNA pattern or

promoter activity (in case of GFP construct) was retained (Fig S5).

4. The obtained patterns were subsequently refined using information of co-expression (Fig.

S5) or based on information on mutual regulation (e.g. AG and AP1 mutually inhibit each

other).

The references and images for each gene are summarized in supplementary file 2 .

In addition, we integrated the four-dimensional gene expression data together with all segmented and

tracked time courses in an open source standalone software platform, called AtlasViewer (available at

https://gitlab.com/slcu/teamHJ/publications/refahi_etal_2020/-/tree/master/atlasviewer/atlasviewer). The

patterns were imported directly from Morphonet into AtlasViewer. Visualization of combination of gene

expressions using AtlasViewer facilitated the identification and correction of annotation errors.

Cell states, clustering and transition graphs

After assigning expression values for the 27 genes to individual cells, this boolean element vector is used

to define a cell state for each cell (Fig. 4A-B). Similarities between cell states were calculated using the

Hamming distance, i.e. the sum of the absolute differences between the vector elements (Fig. 4C). The

states were clustered using hierarchical agglomerative clustering from SciPy package using Ward’s

method, which uses Ward variance minimization algorithm, leading to a dendrogram. Manual flipping at

the dendrogram nodes and identification of tissue structures were applied to generate the final graph

(Fig. 3D).

To illustrate the evolution of cell states over time, cell lineages were used to generate a pattern transition

graph whose vertices were cell states. An arrow connected two vertices if and only if any of the

descendant cells of the source cell state acquired the target cell state at the next developmental stage. We

then assigned weights to arrows as the number of descendant cells in a specific state divided by the total

number of descendant cells. More precisely, let x → y be an arc of the transition graph, where x and y are

cell states. The assigned weight, w, is defined as w = (#descendant cells of cells in pattern x in pattern y) /

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(#descendant cells of cells in pattern x), where # denotes number of cells. To extract the main structure of

the pattern transition graph, we then pruned by keeping the arrows whose weight were equal or greater

than a manually defined threshold of 0.2. However, in this representation the descendent patterns with a

small number of cells are penalized. We therefore also computed a reverse pattern transition graph

where arcs pointed from descendent patterns to their ancestors. For each arrow, x← y, in the reverse

transition graph, where x and y were cells states, we assigned a weight w’, defined as, w’= (#cells in

pattern y whose ancestors are in pattern x) / (#cells of cells in pattern y). The weights were then used to

prune the reverse transition graph by removing the arrows whose weight were below 0.2. The pruned

transition graphs were then merged into a single transition graph, Figure 4.

Cell growth and anisotropy rates and correlation analysis with gene expression and states

Assuming exponential growth of a cell of volume V, , with a constant relative growth rate we𝑑 𝑉𝑑𝑡 = 𝑘𝑉

compute from cell volumes and lineage information for a cell at time point , ( index𝑘 𝑐 𝑡𝑖

0 ≤ 𝑖 ≤ 4

corresponding to the 5 developmental stages considered), as:

,𝑘𝑐, 𝑡

𝑖 → 𝑡

𝑖+1

=(ln(𝑑 ∈𝐷

𝑐

∑ 𝑉𝑑) − ln(𝑉

𝑐)) / (𝑡

𝑖+1− 𝑡

𝑖)

where Vc is the volume of the mother cell , Vd is the volume of a daughter cell d, and is the set of𝑐 𝐷𝑐

daughter cells of at time point .𝑐 𝑡𝑖+1

Projection of computed values on time courses can be done either on the mother cell or on the daughter

cells (e.g. Fig. 5C). Correlation analysis between the computed values and gene expression was done for

cells expressing a specific gene in both forward (following all cells expressing a gene at one time point

to the next) and backward (tracking all cells expressing a gene at a specific time backward in time).

Similar correlation analysis is done for averaging cells within a specific cell state. When both forward

and backward growth are available, the growth rate of a cell at time point was computed as the𝑐 𝑡𝑖

average of the two to quantify growth at a specific time (e.g. Fig. 7C):

) = ,𝑔𝑟(𝑐, 𝑡

𝑖(𝑘

𝑚, 𝑡𝑖−1

→ 𝑡𝑖

+ 𝑘𝑐, 𝑡

𝑖→ 𝑡

𝑖+1

) / 2

where is the mother cell of . In the cases where only one was available, the reported values are for the𝑚 𝑐

first time point the forward growth calculation and for the last time point the backward growth

calculation.

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3D growth anisotropy was computed using cell and lineage information by identifying and matching key

points on the cell and set of daughter cells’ surface. We define key points as the smallest set of points on

the cell surface enveloping the cell (Convex Hull, calculated using Python bindings to QHull library,

http://www.qhull.org/). The Convex Hulls of each cell and its daughter cells were centred and then

mapped according to a nearest neighbour criterion. We then calculated the best (least-squares estimation)

linear transformation between the two hulls:𝐴

,𝑌‾ = 𝐴 𝑋‾ + 𝑏

where is the collection of the selected points for a cell and the collection of corresponding points on𝑋‾ 𝑌‾

the daughter cells’ surface.

The transformation was decomposed into three transformations, two rotations and an expansion using the

Singular Value Decomposition (SVD):

,𝐴 = 𝐷𝑆𝐷𝑇

where and are the rotations and is the expansion. The singular values of ( represent the𝐷 𝐷𝑇 𝑆 𝑆 𝑠1, 𝑠

2, 𝑠

3)

length of the expansion along the axes. The anisotropy is then computed using these expansion lengths

as the fractional anisotropy :𝑎

𝑎 = 32

(𝑠1

−𝑠^)2 + (𝑠

2 − 𝑠

^)2+(𝑠

3 − 𝑠

^)2

𝑠1

2 +𝑠2

2+𝑠3

2

where . The fractional anisotropy is a scalar value ranging from 0 (expansion was𝑠^

= (𝑠1

+ 𝑠2

+ 𝑠3)/3

equal in all directions) to 1 (expansion was in only one direction). The anisotropy rate is the fractional

anisotropy per hour.

Correlation analysis between growth anisotropy and gene expression and states, like in the case of

growth rates, can be done in both forward and backward directions. When both are available the

anisotropy rate at time point was calculated as the average of the forward anisotropy rate calculation𝑡𝑖,

from to and the backward growth anisotropy rate calculation from to .𝑡𝑖

𝑡𝑖+1

𝑡𝑖−1

𝑡𝑖

Regulatory network analysis

We extracted the gene regulatory interactions, inhibition and activation, from the published literaturebased on the available data on direct binding on promoter regions and mutant analyses (Fig. 1).

Boolean regulatory terms

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To analyse the regulatory network, we defined a subset of boolean rules combining the input arrows inthe regulation network (i.e. repression and activation), and examined whether they could reproduce thespatial gene expression patterns of the Atlas. Since the input arrows indicate either positive (activation)or negative (repression) regulation, the corresponding boolean regulatory terms that we define have twosub-terms for activation and repression. We next define the types of terms used for the full regulatoryterm and the repression and activation sub-terms (for further details on network construction see(Moignard et al., 2015)).Regarding notation we assume we have a set of names where range over symbols𝑔

1, 𝑔

2, ... ∈ 𝑆𝑦𝑚𝑏

representing gene names, range over (possibly empty) activation/repression terms,ϵ, 𝑡 , 𝑡 ' ∈ 𝑇𝐸𝑥𝑝

and over full regulatory terms. We will give the following definitions using the ‘is𝑟, 𝑟' ∈ 𝑅𝐸𝑥𝑝𝑟defined as’ symbol ( ) to separate the class being defined (e.g. regulatory expressions) with its:: =definitions and the ‘alternative’ symbol ( ) to separate definitions in cases where there is more than one.|

The class of regulatory interactions for each gene is defined as

,𝑟 :: = 𝑡 ∧ ¬ 𝑡'

where is a full regulatory term for a gene including an activation term ( ) and a𝑟 ∈ 𝑅𝐸𝑥𝑝𝑟 𝑡 ∈ 𝑇𝐸𝑥𝑝repression term ( ) combined by a logical and ( ) and logical not ( ).𝑡' ∈ 𝑇𝐸𝑥𝑝 ∧ ¬

Each term can be empty ( ), a gene name ( syntactic case), or a combination of gene namesϵ 𝑔 ∈ 𝑆𝑦𝑚𝑏with conjunction or disjunction, as described by

𝑡 :: = ε| 𝑔| 𝑡' ∧ 𝑔

,| 𝑡' ∨ 𝑔

where represents a logical or.∨

We next define an evaluation function to evaluate the activation and repression terms to values in the set( for true, and for false). Evaluation happens in a value environment providing values𝐵 = {𝑇, 𝐹} 𝑇 𝐹

(True or False) for the gene names in the terms. To represent this context we use a sequence of genename value bindings where (gene names) andσ = 𝑔

1: 𝑏

1,···, 𝑔

𝑛: 𝑏

𝑛𝑔

1, ···, 𝑔

𝑛 ∈ 𝑆𝑦𝑚𝑏

(True or False representing expression or non-expression of the corresponding gene),𝑏1, ···, 𝑏

𝑛 ∈ 𝐵

where the gene names are required to be distinct. We will sometimes treat this context as a function withfinite domain; for example to obtain the value of in we wrote The evaluation function𝑔

1σ σ(𝑔

1).

in a value environment is then (per syntactic case):[| |] : 𝑇𝐸𝑥𝑝 → 𝐵 σ

[| ϵ |] = 𝐹

[| 𝑔 |](σ) = σ(𝑔)

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[| 𝑡 ∧ 𝑔 |](σ) = [| 𝑡 |](σ) ∧ [| 𝑔 |](σ),[| 𝑡 ∨ 𝑔 |] (σ) = [| 𝑡 |] (σ) ∨ [| 𝑔 |](σ)

where , . For both ’s and ’s evaluation functions, we assume that the𝑡 ∈ 𝑇𝐸𝑥𝑝 𝑔 ∈ 𝑆𝑦𝑚𝑏 𝑇𝐸𝑥𝑝 𝑅𝐸𝑥𝑝𝑟given environments are well-formed, i.e. they contain mappings for all the gene names that appear in theexpression being evaluated. Note that the above evaluation implies left association of expressions so, forexample, the expression is evaluated as .𝑎 ∧ 𝑏 ∨ 𝑐 (𝑎 ∧ 𝑏) ∨ 𝑐

The evaluation function for the full regulatory term is:[| |] : 𝑅𝐸𝑥𝑝𝑟 → 𝐵

[| 𝑡 ∧ ¬ 𝑡' |](σ) = [| 𝑡 |](σ) ∧ ¬[| 𝑡' |](σ)

Two ’s are semantically-equivalent if they contain the same gene names and given the same𝑅𝐸𝑥𝑝𝑟environment they evaluate to the same value.

Translating the gene regulatory network into boolean regulatory terms

Given a gene regulatory network, as in Fig. 1, for each gene we have a set of activators (positiveregulation) and a set of repressors (negative regulation), but there is no information on how their inputscombine to control expression of their target gene. In order to see the most likely boolean regulatoryterm between the regulations, we enumerated all the possible ’s for the activators, all the possible𝑇𝐸𝑥𝑝𝑟

’s for the repressors, combined them into regulatory terms ( ’s) and scored them based on𝑇𝐸𝑥𝑝𝑟 𝑅𝐸𝑥𝑝𝑟how well they agree with the expression data (Supplemental Table 2).

Given a set of input activators/repressors , for a gene there are possible ’s.{𝑔1, ···, 𝑔

𝑛 } 𝑛! · 2𝑛−1 𝑇𝐸𝑥𝑝

For each permutation of the input genes (out of n! possible), we have a choice of disjunction orconjunction between them. For example for 2 activator genes we can generate the following{𝑔

1, 𝑔

2}

terms: . If we also had 2 repressors then the number of terms{𝑔1

∧ 𝑔2, 𝑔

1 ∨ 𝑔

2, 𝑔

2 ∧ 𝑔

1, 𝑔

2 ∨ 𝑔

1 }

becomes 16. While the number grows very quickly with , we found that is not prohibitive for the𝑛number of genes we have here ( .𝑛 < 5)Each cell in a tissue dataset implies a value environment; for example if in a cell gene is on, gene𝑔

1𝑔

2

is off, gene is off, and is off we get a value environment . We can then𝑔3

𝑔4

𝑔1: 𝑇, 𝑔

2: 𝐹, 𝑔

3: 𝐹, 𝑔

4 : 𝐹

evaluate the generated boolean regulatory terms in this environment so for example for an expression for= we can evaluate for that cell𝑔

4(𝑔

1 ∧ 𝑔

2) ∧ ¬𝑔

1

, which (for this example cell) agrees with the[| (𝑔1

∧ 𝑔2) ∧ ¬𝑔

1|](𝑔

1: 𝑇, 𝑔

2: 𝐹, 𝑔

3: 𝐹, 𝑔

4 : 𝐹) = 𝐹

actual value of .𝑔4

Hypotheses generation

In order to generate new hypotheses for each gene, we enumerated all possible changes in the form ofsingle regulatory interactions between genes of the published gene regulatory network. Therefore either

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https://doi.org/10.1101/2020.09.25.313312

existing single interactions were removed or new ones were added. For each modified interaction, wegenerated all possible ’s and full regulatory terms as before.𝑇𝐸𝑥𝑝

Suppose we have a universe of genes Then, for a gene A with two activators𝐺 = {𝑔1, 𝑔

2, 𝑔

3, 𝑔

4}.

and one repressor , the following set of regulatory interactions for that gene would be(𝑔1, 𝑔

2) 𝑔

4

generated: (acts=( , reprs=( )), (acts=( ), reprs=( )), (acts=( ), reprs=( )),{ 𝑔1, 𝑔

2, 𝑔

3) 𝑔

4) 𝑔

1, 𝑔

2𝑔

4, 𝑔

3𝑔

1𝑔

4

(acts=( ), reprs=( )), (acts=( ), reprs=()) . Note that we only added inputs from genes that were𝑔2

𝑔4

𝑔1, 𝑔

2}

not in the original network, whereas the gene , could represent any other gene in the network not yet𝑔3

connected to gene A. For each set of inputs (activators and repressors) we then generated and scoredregulatory terms as before.

Pattern Evaluation

To score an expression pattern generated from cell lineage, the regulatory network of a particular gene(Fig. 1), or a boolean model including hypothesis for an entire tissue, we evaluate it for all the cells andcalculate the Balanced Accuracy (BAcc) for its predictions. BAcc is defined as 1

2 (𝑇𝑁/𝑁 + 𝑇𝑃/𝑃)

where is the number of true negatives (# of cells where the expression evaluates to false and the𝑇𝑁actual value of that gene is false --- like the example above), is the number of true positives (#of cells𝑇𝑃where the expression evaluates to true and the actual value of the gene is true), is the number of𝑃positives (#of cells where the value of the gene is true), and is the number of negatives (# of cells𝑁where the value of the gene is false). We chose BAcc as measure since it also penalizes errors whereonly few cells have an expression (or opposite). We also tried alternative similarity measures, such asMutual Information and % correct. This led to the same conclusions.The scores and therefore the best expressions are not necessarily the same for the tissues at differenttimepoints (Supplemental Table S3). For each gene and each time point we merged and ranked thegenerated regulatory expressions for all the proposed interactions keeping only the ones that are within10% of the best expression for that time point. Starting from the last time point going backwards we thenidentify expressions that appear near the top in more than one time point for a single coherenthypothesis.

Model comparison and random models

In order to establish a baseline for the comparison of ’s generated by the hypotheses, the ’s𝑅𝐸𝑥𝑝𝑟 𝑅𝐸𝑥𝑝𝑟based on the reference network, and lineage prediction, we also constructed a random network with thesame structure as the gene regulatory network in Fig. 1, where all the inputs are replaced with randominputs. For the results reported in the main text we generated 100 random ’s per gene based on𝑅𝐸𝑥𝑝𝑟random inputs with the same numbers as they appear in the gene regulatory network(Fig. 1). These werethen scored (using BAcc) per time point and averaged.All the p-values reported in the main text are the result of a paired t-test between the scores of all thegenes under the different models, e.g. lineage scores vs best hypothesis scores.

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https://doi.org/10.1101/2020.09.25.313312

Growth regulation

In order to examine growth regulation by gene expression we used Relative Growth Difference (RGD) tocompare growth differences between populations of cells (defining regions on a tissue), defined as:

( ) / ( ,𝑟1

− 𝑟2

𝑟1

+ 𝑟2)

where is the median growth rate of the first population of cells and is the median growth rates of the𝑟1

𝑟2

second population of cells. The RGD ranges from 0 to 1 except in some cases early on in developmentwhere it can be > 1 when one of the regions considered has a negative median growth rate.

To examine the gene regulation of growth by the action of single genes, we examined the differencesbetween the population of cells expressing a gene versus the population of cells not expressing the gene.Spatially this defines two regions, which can be described as boolean expressions for a gene, , as and𝑔 𝑔

. Writing for the set of cells where expression is True and for the union of of all¬𝑔 [𝑒]𝑡

𝑒 [𝑒]𝑇

=𝑡

𝑖∈𝑇⋃ [𝑒]

𝑡𝑖

the cells where the expression is True over all time points, the RGD of a gene was calculated as:𝑔

( , T)) / ( , T)),𝑚(𝑔, 𝑇) − 𝑚(¬𝑔 𝑚(𝑔, 𝑇) + 𝑚(¬𝑔

where is the median growth rate of the cells in the regions defined by the𝑚(𝑒, 𝑇) = 1|[𝑒|

𝑇 𝑐 ∈[𝑒]𝑇

∑ 𝑔𝑟(𝑐)

expression, , over a set of time points, . The evaluation of an expression in a cell follows the𝑒 𝑇procedure described in the ‘Boolean regulatory expressions’ section. The growth rate of a cell is, whenpossible, the average of backward and forward growth rates as described above.

In order to get a more fine-tuned understanding of growth gene regulation we extended our single-geneanalysis to pairs of genes that are co-expressed. Each combination of co-expressed genes implicitlydefines two regions (populations of cells) on the flower tissue at any time point. These two regions canbe defined using boolean expressions as, (region where they are co-expressed) and𝑔

1∧ 𝑔

2𝑔

1∧ ¬ 𝑔

2

(region where only one of them is expressed). For each pair of co-expressed genes the RGD at time point(colour maps in the heatmaps in Supp. Figs 11, 12, 13) was calculated as:𝑡

𝑖

) ) ) )( 𝑚(𝑔1∧ 𝑔

2, {𝑡

𝑖}) − 𝑚(𝑔

1∧ ¬ 𝑔

2, {𝑡

𝑖} / ( 𝑚(𝑔

1∧ 𝑔

2, {𝑡

𝑖}) + 𝑚(𝑔

1∧ ¬ 𝑔

2, {𝑡

𝑖}

In order to get the most common regional separation implied by gene pairs at a time point we groupedthe pairs into categories (numbered annotations in the heatmaps in Supp. Figs 11, 12, 13) defining thesame regions. Two pairs of genes and define the same regions at if the two boolean𝑔

1, 𝑔

2 𝑔'

1, 𝑔'

2𝑡

expressions they imply select the same set of cells:

and[𝑔1

∧ 𝑔2]

𝑡 = [𝑔'

1∧ 𝑔'

2]

𝑡 [𝑔

1∧ ¬ 𝑔

2]

𝑡 = [𝑔'

1∧ ¬ 𝑔'

2]

𝑡

24


https://doi.org/10.1101/2020.09.25.313312

In Supp. Figs 11, 12 and 13 we only display the groupings in the top 50% (by RGD) of the pairs at thattime point up to a maximum of 6 groupings. Groupings are also sorted by RGD so the group with index1 has the highest RGD and so on.

Data Availability

Confocal z-stacks, segmentation files, cell lineage information, and in situ hybridisation images areavailable online (doi: provided on acceptance). Software scripts for reproducing the analysis performedin this work is available via the Sainsbury Laboratory gitlab repository(https://gitlab.com/slcu/teamhj/publications/refahi_etal_2019). All data is interactively minable via theMorphoNet ATLAS (http://www.morphonet.org).

Author contribution

Y.R., A.Z., H.J., J.T. designed research; Y.R., A.Z., R.W., G.M., J.L.,H.J., J.T., A.A., L.V., A-E.R., P.D.and F.Z. performed research; Y.R.,A.Z., H.J., J.T., R.W., G.M., J.L., N.P., F.B., C.G., E.M., G.Ma.,contributed new reagents/analytic tools; Y.R., H.J., J.T., A.Z., G.M., J.L, G.Ma., A.A., L.V. and P.D.analyzed data; Y.R.,A.Z., H.J., J.T. wrote the paper.

Acknowledgements

The authors would like to thank Arun Sampathkumar, OIivier Hamant and Marie Monniaux fordiscussion, Anuradha Kar for help with MorphoNet. Weibing Yang provided the lfy mutant and helpedwith imaging. JT, YR, AA, LV, A-ER and FZ were funded by the ERC grant MORPHOGENETICS.This work was also supported by ANR BIOMOD (ANR-19-CE43-0010) grant (to YR.) and Gene2ShapeERACAPS grant to JT, HJ and AZ. The E.M.M laboratory is funded by the Howard Hughes MedicalInstitute, and the work here was supported by the U.S. National Science Foundation Division ofIntegrative Organismal Systems grant IOS1826567.

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https://gitlab.com/slcu/teamhj/publications/refahi2019

http://www.morphonet.org

jtraas

HJ was funded by the Gatsby Charitable Foundation (GAT3395/PR4B) BBSRC (BB/S004645/1)

https://doi.org/10.1101/2020.09.25.313312

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Figure 1. Gene regulatory network proposed for flower patterning and morphogenesis. Red and blue

connections represent negative and positive regulations respectively. Colour code indicates function in

floral meristem development, floral organ identity (sepals, petals, stamens and carpels) and

abaxial/adaxial organ polarity as described in the litterature. The regulators in light blue characters are

not recorded in the current version of the Atlas because there is not sufficient information on their

expression patterns.

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Figure 2. Cell lineage in reference series. 8 out of 18 timepoints of FM1 are shown. Times after firstacquisition are indicated between brackets. (A) Surface rendering of segmented images of time course 1showing L1 layer cells. (B) Surface rendering of segmented images showing L2 cells (L1 cells areremoved. Cells are colored according to computed lineages. Scale bars in A and B 20 um

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Figure 3. (A) Matrix representing 32 combinatorial, binary expression patterns (referred to as ‘states’) of28 genes. WUS, which is only expressed in internal tissues, is not represented. Each row corresponds to aparticular state (state numbers are given on the left) and contains black (gene active) and white (geneinactive) squares. Names of the genes are given on top of each column. (B) Rendering of geneexpression patterns in the L1 layer. Each of the patterns are colored by a unique color and their

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corresponding codes are also given. B.1., B.2., B.3., B.4., and B.5 correspond respectively to intium,stage 1, stage 2, stage 3, and stage 4 time points. Grey cells have not been annotated (no expression). (C)Hierarchical clustering of cell states using Hamming distances as the measure of similarity. The heatmap (similarity matrix) corresponds to the Hamming distances and the columns and rows are thepatterns. D) Individual clusters or combinations of clusters correspond to specific differentiation domains(organ identity for example) in the growing flower (color coded). Alternatively, the clusters can beassigned to more general ‘functional’ domains not specific for the flower (meristem, boundary domains).

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Figure 4. Temporal evolution of clusters and cell states. The graph combines ‘forward’ and ‘backward’links. Forward links connect specific states at one time point to their descendant patterns in the next timewith weights corresponding to the fractions of the daughter cells in each of the descendant patterns.Similarly ‘backward’ links identify states at a previous time point from a current one. Arcs with bluearrows indicate the presence of corresponding arcs both in forward and reverse pattern transition graphs,dashed arrows indicate the presence of corresponding arcs in reverse pattern transition graph only, redarrows indicate the presence of corresponding arc forward patterns transition graph only (see alsosupplementary figures). The links whose weights were below a threshold of 20% were pruned.

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Figure 5: Expected patterns vs predicted patterns from various models. (A) Example geneexpression patterns at stage 4 (132h). Data from the template (top row) is compared with predictedpatterns coming from: Following cell lineages from stage 3 (second row), boolean regulatory modelfrom literature network (Fig. 1, third row), and boolean regulatory model where an additional regulatoryarrow has been added as hypothesis (Table S4, fourth row). Numbers above the illustrations indicate theBAcc score. Below the illustrations either the selected combination of inputs (in the case of the literaturebased boolean model) or the selected best hypothesis (in the case of the augmented literature booleanmodel) is shown. (B) BAcc score for all genes using the methods of lineage, literature network withrandomised input (see Methods), literature network regulatory model (Fig. 1), and model with addedhypotheses. Result of best hypothesis given for each Stage of flower development (C) Average (andstandard deviation) of BAcc score over all time points and genes for the same conditions as described in(B). (D) Gene by gene comparison of BAcc scores between literature network (ref) and lineage (lin) atstage 4. (E) Gene by gene comparison of BAcc scores between literature derived network (Fig 1) andafter adding regulatory hypothesis (hyp) at stage 4.

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Figure 6. Relative growth rates for single cell clones. (A) Relative volumetric growth rates per hour ofL1 cells, indicating how much the cells have grown. Color scale bar from nongrowing (black) to morerapidly growing cells (yellow/white) in um3/h. L1 cells with positive, relative growth rates are displayed.Light grey cells are not taken into account. (B) Growth anisotropy of L1 cells. Color scale indicatesdegree of anisotropy per hour (see methods). Light grey cells are not taken into account.(C) Distribution of growth rates (um3/h vs number of cells) between different time points. Note that thenumber of cells followed between timepoints can differ, depending on the available, tracked lineage (D)Relative volumetric growth rates per hour of L1 cells between 10-132h (upper panel) and 96 and 132h(lower panel). Color code on initium and stage 2 indicates how much the cells will grow. Color code onstage 4 how much the cells have grown. At 96h the cell lineage and increased growth rates of the sepalsare already largely fixed. Two cells have not grown between stage 2 and 4, so their contribution musthave been taken over by neighboring cells.Note: growth rates and degree of anisotropy are taking into account both forward and backwardrates (i.e. how much the cells have grown and how much they will grow). This is not the case forthe first and last point, where resp only forward and backward growth is presented.

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Figure 7. Growth rates correlated with gene expression and cell states. (A) Relative growth rates perhour in expression domains of individual genes, (B) Growth rates of combinatorial patterns or cell states,numbered as in Fig 4. Note that the growth rates were calculated from one point to the next point(forward), only the values of the last time point are calculated backwards (marked with *). (C) Growthon the pattern transition graph calculated as the average of the backward and forward rates, exceptinitium stage, only forward and stage 4 only backward (arrows colored as in Fig. 5).

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Fig 8. Analysis of growth rates in cell states and gene expression domains (A) and (B.) Correlatinggrowth with gene function. The growth of cells expressing gene A+ B is compared with the growth ofthose only expressing A. Two examples are given in (A) Within the ETTIN (gene A) expressing domain,the cells expressing STM (gene B) as well are growing more slowly; within the AP1 domain, the LFYcells are growing more quickly. (B). The results for all gene combinations. Values correspond to theRGD calculated using the median values of the growth distributions. Certain genes are mostly expressedin the more rapidly growing subdomains (e.g. LFY, AHP6, ANT), others mostly in the slowly growingsubdomains (e.g. SEP3, AG, CUC1-3). The darker blue the spots correspond to later time points.C. Current and future growth rates of different domains at stage 2 of flower development. Currentgrowth rates are relatively homogeneous in state 10 (orange zone) vs the other states (8, 9, 11, 12, bluezone). However the states in the blue zone will grow much more quickly afterwards, resulting in theoutgrowth of the sepals.

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Figure 9. Growth anisotropy correlated with gene expression and cell states. (A) 3D growthanisotropy rate of expression domains of individual genes. (B) Growth anisotropy/hour in combinatorialpatterns or cell states (numbering as in fig 4). Note that the values were calculated from one point to thenext point (forward), only the values of the cell states of the last time point are calculated backwards(marked with *). (C) Growth anisotropy on the pattern transition graph calculated as the average of thebackward and forward anisotropy rate (except initium stage, only forward and stage 4 only backward).

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Fig 10. Comparison growth patterns in wildtype (wt) and lfy mutant (lfy). (A) part of the time series ofthe lfy-12 mutant (see also Fig S16), equivalent to stage 2, 3 and 4 in WT. (B) Comparisons of growthrates between different equivalent regions in WT and lfy mutant at stage 4 (cf Fig 8 and S13-14). Blueand red histograms correspond to red and blue zones indicated in images. Combinations of regions arenumbered 1-6. (C) Plot integrating relative growth differences (RGD: median blue graph - median redgraph)/(median blue graph + median red graph) in WT and lfy mutant combinations 1-3 at stage 3 and 4.(D) Plot showing medians lfy/wt (blue median/blue median, red median/red median).In lfy, the medians of the blue and red histograms are systematically closer to each other than in wildtype, hence the growth differential is reduced. Scale bars in A: 20 um.

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a multiscale analysis of early flower development in arabidopsis … · 2020. 9. 25. · a...

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